1.4: Showing Students' Thinking
- Page ID
- 90467
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Ways to Help Students “Show Their Thoughts” on Paper
Here are six methods, which can help students organize their thoughts. It is recommended that the teacher says to the students: “Show your thoughts” instead of “Show your work”. This change encourages students to write more on the paper.
Method 1: Inquiry
Before you teach a new concept, have students fill out the Inquiry Box below. Have the students write or draw any observations. (I see…) What inferences do they have? (I think…) Describe your prior knowledge. (I know…)
Method 2: Four-Square Chart
Use to review learned vocabulary.
Method 3: Note Taking
Method 4: Concept Web
Use a Concept Web to solve different types of problems which all have something in common. For example, “Fill in the Blank” can have students look at different patterns and fill in the missing piece of the pattern.
Method 5: Problem-Solving Strategy
Given a word problem, students can fill out this table to help them decode the word problem and figure out how to set up and solve the problem.
Method 6: A Five-Step Formula
Use this method to solve complicated word problems.
Classroom Instruction and Discussions
Method 1: Elbow Buddies
Kids get a kick out of this method. “Now talk with your elbow buddy,” is an instruction where they can only talk with the person who sits next to them, touching elbow to elbow. This works well when the students are seated in pairs or groups of four.
Method 2: Think-Pair-Share
This method is very popular, easy, and has been around for a long time – because it works! To start a deep discussion with your students they need to be prepared.
Pose the question to your students. Have them take some predetermined time to THINK about their answer. No talking. No writing. No researching. Just thinking. Have them share their thoughts with their Elbow Buddy. Only a PAIR of students should be whispering their thoughts back and forth. Then ask the class to raise their hands if they would like to SHARE what they thought of or what their Elbow Buddy thought of.
Method 3: Cooperative Learning
Cooperative Learning is very important in Common Core mathematics learning. Students need to share ideas. Having students work on group projects and group presentations will help them be successful in high school and beyond.
Method 4: Direct Instruction
Direct instruction is when the teacher is in the front of the classroom and the students are silently taking notes. There is very little interaction.
One of the founders/authors of the original Common Core idea said that Direct Instruction should be about 20% of total learning. 80% of the time, students should be working in some other fashion. Use direct instruction when the students need to learn a difficult topic.
Method 5: Guided Instruction
Guided Instruction is better than Direct Instruction. With Guided Instruction, the students are interacting with the teacher. The teacher will ask questions to lead the instruction and learning.
Method 6: Inquiry
With Inquiry, students come up with their own questions about what is presented in front of them. Most of the time, this method is used in Science, but it can also be used in mathematics.
Technology Resources for Your Classroom
And it is all FREE!! Or most times, the school will have a subscription, so it is free for you.
Khan Academy
Khan Academy is more than just mathematics. Many subjects are found on this free website. Not only will it be a semester long project for you, but I hope you use this website in your future classroom to help your future students keep up in mathematics.
See Canvas for Math 130’s instructions for your semester long project
Google Classroom and Google Forms
In this technology society, it makes sense for students to take exams online. With Google Classroom, a Chromebook and Google Forms, students can take an exam online; where Google locks the Chromebook. Students are not able to visit any other websites while taking the assessment. If they try, Google will cut their assessment score in half and send the teacher an email.
You Tube
It has been said that one can learn anything on YouTube. And it is true. Use YouTube in your classroom to show videos which might help the students “by-in” to what you are trying to teach them.
edPuzzle
This is a wonderful resource. Teachers and students can use to make videos.
Dreambox
This is a fun game based website where the students have to solve grade level appropriate math problems to advance on to the next level and earn gold coins.
ABCya!
Another game based website where the students must solve the math problem to advance. Here the students’ games can be assigned by Common Core standards.
Zipgrades
Zipgrades are the new version of scantrons. You use their paper (free download) and your phone to grade their scantron. Works great most of time, to be honest. But if your school does not have a scantron machine, this could be the next best option.
Desmos
Desmos.com is a mathematicians dream come true. It can graph virtually anything. This is a great teaching tool if your classroom has a smart board and you are teaching pre-algebra in 6th grade.
Geometers Sketchpad
Another great tool for teachers. Easily make geometry shapes. Ask your school to buy a license.
Kuta Software
Kuta makes “drill and kill” worksheets for grades 5 and 6 (it is mostly used for junior high and high school teachers.) Free, already made, worksheets can be found at kutasoftware.com. To make your own worksheets, have your school buy the license.